Simplify the following expression: $\dfrac{12r^2}{18r^4}$ You can assume $r \neq 0$.
$ \dfrac{12r^2}{18r^4} = \dfrac{12}{18} \cdot \dfrac{r^2}{r^4} $ To simplify $\frac{12}{18}$ , find the greatest common factor (GCD) of $12$ and $18$ $12 = 2 \cdot 2 \cdot 3$ $18 = 2 \cdot 3 \cdot 3$ $ \mbox{GCD}(12, 18) = 2 \cdot 3 = 6 $ $ \dfrac{12}{18} \cdot \dfrac{r^2}{r^4} = \dfrac{6 \cdot 2}{6 \cdot 3} \cdot \dfrac{r^2}{r^4} $ $\phantom{ \dfrac{12}{18} \cdot \dfrac{2}{4}} = \dfrac{2}{3} \cdot \dfrac{r^2}{r^4} $ $ \dfrac{r^2}{r^4} = \dfrac{r \cdot r}{r \cdot r \cdot r \cdot r} = \dfrac{1}{r^2} $ $ \dfrac{2}{3} \cdot \dfrac{1}{r^2} = \dfrac{2}{3r^2} $